1882.] W. Spottiswoode. On Russell's Integrals. 341 



February 9, 1882. 



THE PRESIDENT in the Chair. 



The Right Hon. Henry ^Fawcett was admitted into the Society. 



The Presents received were laid on the table and thanks ordered for 

 them. 



The following Papers were read : — 



I. " Note on Mr. Russell's paper, ' On certain Definite Integrals. 

 No. 10.' " By William Spottiswoode, M.A., D.C.L, LL.D., 

 Pres. R.S. Received January 30, 1882. 



If in Mr. Russell's paper* we take the standard forms — 

 O, b, . . .)(*, 1) 4 =0, (3, 7 )(X^ + 2 ^ + v, 1)2, 

 we shall have for eliminating «, /3, 7, X, /n, v, the five equations : — - 



b = a\ju, 

 3c = 2ot[ir l + aXv + ft\ 



e= a v 2 + 2y3^ + 7, 



the last of which alone contains 7, and may therefore be omitted for 

 the present purpose. Combining the remaining equations, it will be 

 found that 



from which both /3 and v have simultaneously disappeared. Hence we 

 have the three equations — 



a : \?=b : \jll= (Scfi—dX) : /r 3 , 



for the elimination proposed. These readily give — 



a*d-3abc + 2tf=0. 



Again, for the sextic — 



(a, b, . . 00, iy=(*, & 7, s)CKx*+2fix+p, iy y 



* " Proc. Roy. Soc," vol. 33, p. 258. 



